On world Drachenfels I used one of my free reroll items for the resource deposit. The game took my item (i originally had 2 not only 1) but did not give me any new errands at the resource deposit.
from what i can tell it doesnt give you new errands to do if you have already done all your errands i think its more like if you have errands already that are all 1 star and you want a chance at better stars or if all the resources they offer are not the ones you want you can "reroll" your current errands to try and get something different or better
It looks like that is what it is supposed to do. I used 2 re-rolls I had (to test this), but I got the same resources both times. either way it's broken.